I thought is was a strange question. Just to confirm, for complex numbers the same laws for real numbers for exponents holds right? so for complex a,b,c (a^bc) = (a^b)^b ?

I assume you meant (ab)c = abc. That identity is valid only for positive real a and real b and c. The ultimate point of this exercise is to show that this identity no longer holds for complex a, b, and c.

Another one to watch out for is the identity (ab)c = acbc. This, too, is no longer valid for complex a, b, and c.

I assume you meant (ab)c = abc. That identity is valid only for positive real a and real b and c. The ultimate point of this exercise is to show that this identity no longer holds for complex a, b, and c.

Another one to watch out for is the identity (ab)c = acbc. This, too, is no longer valid for complex a, b, and c.

For (ab)c = acbc if a and b are real but c is complex would it still hold?